The Reds have rejected two bids from their Premier League rivals for the England international, the last amounting to £40million, as they value the 20-year-old at £50million.
However, with most of the players scheduled to return to pre-season training next week Aldridge insists now is the time to cash in on the youngster – who has turned down a £100,000-a-week contract offer.
“Brendan Rodgers should let Raheem Sterling leave for Manchester City now,” he wrote on sports social network Kicca.
“The sooner he leaves the better for all involved. All this transfer talk is making a mockery of Liverpool Football Club.
“Raheem is obviously a hugely talented player but Liverpool have a top replacement in Jordon Ibe.
“I think he’s got as much, if not more, potential than Raheem and will go on to be a better player.
“Sterling is obviously too young to think for himself so his agent (Aidy Ward) has been doing his thinking for him.
“For the sake of Liverpool Football Club they should take the millions on offer and then everybody will be better off.
“Raheem will be a bit richer and Liverpool will be rid of a player who doesn’t want to play for the club. It’s a win-win.
“Manchester City are a big club and Raheem will get paid well and play Champions League football so he will be happy.”